Advances in Imaging and Electron Physics, Vol. 124 by Peter W. Hawkes

By Peter W. Hawkes

The 4 surveys contained during this quantity illustrate broadly different facets of imaging and electron physics. the 1st chapters handle purposes of electron microscopy, together with the position of this system in mineralogy and a examine of the excessive- answer electron microscopy of quasicrystals. The latter is de facto a quick monograph providing the underlying crystallography and explaining intimately how the corresponding pictures and diffraction styles could be interpreted. The 3rd contribution is an account of a brand new method of deconvolution in photo processing during which the writer, via associating a polynomial with the gray-level values of (discrete) pictures, indicates that it really is attainable to invert the convolutional relation that describes many varieties of photo formation. the amount ends with a close dialogue of the twin de Broglie wave, together with a serious account of latest advancements within the debate over the life and position of the sort of wave.

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So even if the filter coefficient vector is not directly evaluated, we can still apply this algorithm for system identification as well as for prediction and filtering. In particular a direct dependency of the forward a priori prediction error at time n from the input sample at the same time makes the algorithm suitable for the ADPCM application in signal coding, as is shown in Section VI, even if this direct dependency is paid for with a structure that cannot be pipelined because of the presence of sums of products.

A general approach for blind equalization and identification of nonlinear single-input multiple-output truncated Volterra filters is presented in the aforementioned paper. Although impossible with a single output, deconvolution of blindly multiple truncated Volterra channels is possible with multiple outputs. The approach requires some conditions on the input sequence and the channel transfer matrix. The important result is that the nonlinear channels are equalized with linear FIR filters. This fact can be justified intuitively because the vector equalizer can be seen as a beam former which, because of its diversity, is capable of nulling the nonlinearities and equalizing the linear part.

Second, the novel algorithm is derived, and, third, some experimental results that substantiate the good numerical performance of the algorithm are presented. A. 1. Let d(k) be the desired response signal. The objective is to compute the coefficient V-vector wn in such a way that the filter output is as close as possible to the desired response signal. This V-VECTOR ALGEBRA AND VOLTERRA FILTERS 31 leads to minimizing the exponentially weighted cost function n Jn = k=0 λn−k |d(k) − wnT xk |2 (43) at each time instant n, where λ is a forgetting factor that controls the speed of tracking time-varying signals.

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